共查询到20条相似文献,搜索用时 15 毫秒
1.
For Seifert homology spheres, we derive a holomorphic function of K whose value at integer K is the sl
2 Witten–Reshetikhin–Turaev invariant, Z
K
, at q= exp 2πi/K. This function is expressed as a sum of terms, which can be naturally corresponded to the contributions of flat connections
in the stationary phase expansion of the Witten–Chern–Simons path integral. The trivial connection contribution is found to
have an asymptotic expansion in powers of K
−1 which, for K an odd prime power, converges K-adically to the exact total value of the invariant Z
K
at that root of unity. Evaluations at rational $K$ are also discussed. Using similar techniques, an expression for the coloured
Jones polynomial of a torus knot is obtained, providing a trivial
connection contribution which is an analytic function of the colour. This demonstrates that the stationary phase expansion
of the Chern–Simons–Witten theory is exact for Seifert manifolds and for torus knots in S
3. The possibility of generalising such results is also discussed.
Received: 26 October 1998 / Accepted: 1 March 1999 相似文献
2.
Dirk Blömker Stanislaus Maier-Paape Thomas Wanner 《Communications in Mathematical Physics》2001,223(3):553-582
This paper gives theoretical results on spinodal decomposition for the stochastic Cahn–Hilliard–Cook equation, which is a
Cahn–Hilliard equation perturbed by additive stochastic noise. We prove that most realizations of the solution which start
at a homogeneous state in the spinodal interval exhibit phase separation, leading to the formation of complex patterns of
a characteristic size.
In more detail, our results can be summarized as follows. The Cahn–Hilliard–Cook equation depends on a small positive parameter
ε which models atomic scale interaction length. We quantify the behavior of solutions as ε→ 0. Specifically, we show that
for the solution starting at a homogeneous state the probability of staying near a finite-dimensional subspace ?ε is high as long as the solution stays within distance r
ε=O(ε
R
) of the homogeneous state. The subspace ?ε is an affine space corresponding to the highly unstable directions for the linearized deterministic equation. The exponent
R depends on both the strength and the regularity of the noise.
Received: 2 May 2000 / Accepted: 8 July 2001 相似文献
3.
Invariants for framed links in S
3 obtained from Chern–Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct
a three-manifold invariant. This is a generalization of a similar construction developed earlier for SU(2) Chern–Simons theory. The procedure exploits a theorem of Lickorish and Wallace and also those of Kirby, Fenn and Rourke
which relate three-manifolds to surgeries on framed unoriented links. The invariant is an appropriate linear combination of
framed link invariants which does not change under Kirby calculus. This combination does not see the relative orientation
of the component knots. The invariant is related to the partition function of Chern–Simons theory. This thus provides an efficient
method of evaluating the partition function for these field theories. As some examples, explicit computations of these manifold
invariants for a few three-manifolds have been done.
Received: 24 July 2000 / Accepted: 19 September 2000 相似文献
4.
X. Liu 《Communications in Mathematical Physics》2001,216(3):705-728
We study some necessary and sufficient conditions for the genus-1 Virasoro conjecture proposed by Eguchi–Hori–Xiong and S.
Katz.
Received: 22 August 1999 / Accepted: 7 October 2000 相似文献
5.
We introduce a new 2-parameter family of sigma models exhibiting Poisson–Lie T-duality on a quasitriangular Poisson–Lie group
G. The models contain previously known models as well as a new 1-parameter line of models having the novel feature that the
Lagrangian takes the simple form , where the generalised metric E is constant (not dependent on the field u as in previous models). We characterise these models in terms of a global conserved G-invariance. The models on G=SU
2 and its dual G
* are computed explicitly. The general theory of Poisson–Lie T-duality is also extended, notably the reduction of the Hamiltonian
formulation to constant loops as integrable motion on the group manifold. The approach also points in principle to the extension
of T-duality in the Hamiltonian formulation to group factorisations D=G⋈M, where the subgroups need not be dual or connected to the Drinfeld double.
Received: 22 August 1999 / Accepted: 4 February 2000 相似文献
6.
7.
For operators with a discrete spectrum, {λ
j
2}, the counting function of λ
j
's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑
j
δλ
j
((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ
j
∈ℂ+, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that
where ωℂ+ is the harmonic measure of the upper of half plane and δ can be taken dependent on λ. This provides a precise high energy
version of the Breit–Wigner approximation, and relates the properties of s (λ) to the distribution of resonances close to the real axis.
Received: 16 October 1998 / Accepted: 28 January 1999 相似文献
8.
In the inviscid limit the generalized complex Ginzburg–Landau equation reduces to the nonlinear Schr?dinger equation. This
limit is proved rigorously with H
1 data in the whole space for the Cauchy problem and in the torus with periodic boundary conditions. The results are valid
for nonlinearities with an arbitrary growth exponent in the defocusing case and with a subcritical or critical growth exponent
at the level of L
2 in the focusing case, in any spatial dimension. Furthermore, optimal convergence rates are proved. The proofs are based on
estimates of the Schr?dinger energy functional and on Gagliardo–Nirenberg inequalities.
Received: 2 April 1999 / Accepted: 29 March 2000 相似文献
9.
Denis Perrot 《Communications in Mathematical Physics》2001,218(2):373-391
We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local
conformal diffeomorphisms. After defining a K-cycle on the crossed product C
0(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem
of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism
group of the von Neumann algebra L
∞(Σ)⋊Γ.
Received: 1 February 2000 / Accepted: 3 December 2000 相似文献
10.
We consider weighted traces of products of intertwining operators for quantum groups U
q
(?), suitably twisted by a “generalized Belavin–Drinfeld triple”. We derive two commuting sets of difference equations – the
(twisted) Macdonald–Ruijsenaars system and the (twisted) quantum Knizhnik–Zamolodchikov–Bernard (qKZB) system. These systems
involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler ([ESS]). When the generalized
Belavin–Drinfeld triple comes from an automorphism of the Lie algebra ?, we also derive two additional sets of difference
equations, the dual Macdonald–Ruijsenaars system and the \textit{dual} qKZB equations.
Received: 20 March 2000 / Accepted: 11 December 2000 相似文献
11.
Fraydoun Rezakhanlou 《Communications in Mathematical Physics》2000,211(2):413-438
We study the asymptotic behavior of , where u solves the Hamilton–Jacobi equation u
t
+H(x,u
x
) ≡ 0 with H a stationary ergodic process in the x-variable. It was shown in Rezakhanlou–Tarver [RT] that u
ɛ converges to a deterministic function provided H(x,p) is convex in p and the convex conjugate of H in the p-variable satisfies certain growth conditions. In this article we establish a central limit theorem for the convergence by
showing that for a class of examples, u
ɛ(x,t) can be (stochastically) represented as
, where Z(x,t) is a suitable random field. In particular we establish a central limit theorem when the dimension is one and , where ω is a random function that enjoys some mild regularity.
Received: 15 February 1999 / Accepted: 14 December 1999 相似文献
12.
We extend our variant of mirror symmetry for K3 surfaces [GN3] and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces with some special Picard lattices. These two classes are related with automorphic forms on IV type domains which we studied in our papers [GN1]-[GN6]. Conjecturally these automorphic forms take part in the quantum intersection pairing for model A, Yukawa coupling for model B and mirror symmetry between these two classes of Calabi-Yau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced Calabi-Yau manifolds. Our papers [GN1]-[GN6] and [N3]-[N14] give hope that this is possible. They describe possible Picard or transcendental lattices of general K3 fibers of the Calabi-Yau manifolds. 相似文献
13.
We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC
2
n
(B) and K
0 (B). This reformulation allows us to show that a Hopf–Galois extension admitting a strong connection is projective and left
faithfully flat. It also enables us to conclude that a strong connection is a Cuntz–Quillen-type bimodule connection. To exemplify
the theory, we construct a strong connection (super Dirac monopole) to find out the Chern–Connes pairing for the super line
bundles associated to a super Hopf fibration.
Received: 8 March 2000 / Accepted: 5 January 2001 相似文献
14.
F. Finster N. Kamran J. Smoller S.-T. Yau 《Communications in Mathematical Physics》2002,230(2):201-244
The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial
data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays
in at least at the rate t
−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].
Received: 20 August 2001 / Accepted: 22 January 2002
RID="*"
ID="*"Present address: NWF I – Mathematik, Universit?t Regensburg, 93040 Regensburg, Germany.?E-mail: felix.finster@mathematik.uni-regensburg.de
RID="**"
ID="**"Research supported by NSERC grant # RGPIN 105490-1998.
RID="***"
ID="***"Research supported in part by the NSF, Grant No. DMS-0103998.
RID="****"
ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30. 相似文献
15.
We construct an integral representation of solutions of the Knizhnik–Zamolodchikov–Bernard equations, using the Wakimoto modules.
Received: 5 October 1998 / Accepted: 8 February 1999 相似文献
16.
Krzysztof Burdzy Robert Hołyst Peter March 《Communications in Mathematical Physics》2000,214(3):679-703
We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions.
Received: 11 November 1999 / Accepted: 19 May 2000 相似文献
17.
Karl Haller 《Communications in Mathematical Physics》2000,210(3):703-731
We determine the large U ground states in the neutral two-dimensional Falicov-Kimball model for a sequence of densities converging to 0. For rational densities in (1/6,2/11) we show that the ground states exhibit a phase separation. 相似文献
18.
Charles F. Doran 《Communications in Mathematical Physics》2000,212(3):625-647
Arithmetic properties of mirror symmetry (type IIA-IIB string duality) are studied. We give criteria for the mirror map q-series of certain families of Calabi–Yau manifolds to be automorphic functions. For families of elliptic curves and lattice
polarized K3 surfaces with surjective period mappings, global Torelli theorems allow one to present these criteria in terms
of the ramification behavior of natural algebraic invariants – the functional and generalized functional invariants respectively.
In particular, when applied to one parameter families of rank 19 lattice polarized K3 surfaces, our criterion demystifies
the Mirror-Moonshine phenomenon of Lian and Yau and highlights its non-monstrous nature. The lack of global Torelli theorems
and presence of instanton corrections makes Calabi–Yau threefold families more complicated. Via the constraints of special
geometry, the Picard–Fuchs equations for one parameter families of Calabi–Yau threefolds imply a
differential equation criterion for automorphicity of the mirror map in terms of the Yukawa coupling. In the absence of instanton
corrections, the projective periods map to a twisted cubic space curve. A hierarchy of “algebraic” instanton corrections correlated
with the differential Galois group of the Picard–Fuchs equation is proposed.
Received: 14 August 1999 / Accepted: 30 January 2000 相似文献
19.
We show that for a generic C1 expanding map T of the unit circle, there is a unique equilibrium state for − log T′ that is an S–R–B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of
whether a generic C1 expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure.
Received: 8 December 2000 / Accepted: 27 March 2001 相似文献
20.
G. Eskin 《Communications in Mathematical Physics》2001,222(3):503-531
We consider the Schr?dinger equation in R
n
, n≥ 3, with external Yang–Mills potentials having compact supports. We prove the uniqueness modulo a gauge transformation of
the solution of the inverse boundary value problem in a bounded convex domain. A similar uniqueness result holds for the inverse
scattering problem at a fixed energy.
Received: 11 August 2000 / Accepted: 24 May 2001 相似文献